# An object with a mass of 5 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= xe^x-x . How much work would it take to move the object over x in [1, 4], where x is in meters?

Feb 12, 2016

$W = 147 , 15 \left(3 {e}^{x} - 7\right) J$

#### Explanation:

$W = {F}_{f} \cdot x = N {\int}_{1}^{4} \left(x {e}^{x} - x\right) x \cdot d x$
$W = m g {\int}_{1}^{4} \left({x}^{2} {e}^{x} - {x}^{2}\right) d x$
$W = m g \left({\left[{e}^{x} \left({x}^{2} - 2 x + 2\right)\right]}_{1}^{4} - {\left[\frac{1}{3} {x}^{3}\right]}_{1}^{4}\right)$
$W = m g \left(9 {e}^{x} - 21\right)$
W=5*9,81(9e^x-21#
$W = 147 , 15 \left(3 {e}^{x} - 7\right) J$